Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 2.3 W/m · °C, and surface area A = 20 m^2. The left side of the wall is maintained at a constant temperature of T1 = 90°C while the right side loses heat by convection to the surrounding air at T∞ = 25°C with a heat transfer coefficient of h = 40 W/m^2· °C. Assuming constant thermal conductivity and no heat generation in the wall:
(a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall.
(b) Obtain a relation for the variation of temperature in the wall by solving the differential equation.
(c) Evaluate the rate of heat transfer through the wall.